The 21-year-old Kenyan international is in high demand after a number of impressive performances for the SPL champions, most recently in Wednesday night's 2-1 Champions League victory over Barcelona.
Wanyama scored his side's first goal, and successfully negated the threat posed by Xavi and Andres Iniesta, in what was an imposing display on a memorable night at Celtic Park.
His performance was taken in by Red Devils chief European scout, Martin Ferguson, brother of Sir Alex, who is keen to bring the midfielder to Old Trafford when the transfer window reopens in January.
Gunners boss Arsene Wenger has also been credited with an interest in the African, who arrived at Parkhead from Belgian side Beerschot for a paltry £900,000 fee last year. His overwhelming success in Scotland prompted Bhoys boss Neil Lennon to claim last week that Wanyama is now worth £25million.
However, Manchester United are expected to test the water with a £12million bid in January for a player that remains under contract at Celtic until 2014.
Wanyama has already turned down a contract extension with the Hoops, which will encourage Arsenal and his other admirers, as he considers his long-term future.